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# Coupled Crack /Contact Analysis for Composite Material Containing Periodic Cracks under Periodic Rigid Punches Action

Yue-Ting Zhou1, Xing Li2, De-Hao Yu3, Kang Yong Lee1,4

School of Mechanical Engineering, Yonsei University, Seoul 120-749, Republic of Korea
School of Mathematics and Computer Science, Ningxia University, Yinchuan 750021, China
LSEC, ICMSEC, Academy of Mathematics and Systems Science, CAS, Beijing 100190, China
Corresponding author. Tel./fax: +82 2 2123 2813(K.Y. L). E-mail: zhouyueting (Y.T. Zhou), KYL2813@yonsei.ac.kr (K.Y. Lee).

Computer Modeling in Engineering & Sciences 2010, 63(2), 163-190. https://doi.org/10.3970/cmes.2010.063.163

## Abstract

In this paper, a coupled crack/contact model is established for the composite material with arbitrary periodic cracks indented by periodic punches. The contact of crack faces is considered. Frictional forces are modeled to arise between the punch foundation and the composite material boundary. Kolosov-Muskhelisvili complex potentials with Hilbert kernels are constructed, which satisfy the continuity conditions of stress and displacement along the interface identically. The considered problem is reduced to a system of singular integral equations of first and second kind with Hilbert kernels. Bounded functions are defined so that singular integral equations of Hilbert type can be transformed to Cauchy type. Numerical analyses are conducted through two examples. The presented approach allows considering various configurations of cracks and the punches foundation. Classic results can be obtained when the basic period → ∞(a > 0).

## Keywords

Zhou, Y., Li, X., Yu, D., Lee, K. Y. (2010). Coupled Crack /Contact Analysis for Composite Material Containing Periodic Cracks under Periodic Rigid Punches Action. CMES-Computer Modeling in Engineering & Sciences, 63(2), 163–190.

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